Device for determining an angle from a set of orthogonal components



Aug. 30, 1966 H D. COOK 3,270,189

DEVICE FOR DETERMINING AN ANGLE FROM A SET OF ORTHOGONAL COMPONENTS Filed July 7, 1961 3 Sheets-Sheet l Fly] F59", Z I 5 A? 22 :F

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DEVICE FOR DETERMINING AN ANGLE FROM A SET OF ORTHOGONAL COMPONENTS Filed July 7, 1961 3 Sheets-Sheet 2 INVENTOR Herberffl Cook ATTORNEY Aug. 30, 1966 Filed July 7, 1961 H. D. DEVICE FOR DETERMINING COOK OF ORTHOGONAL COMPONENTS AN ANGLE FROM A SE Sheets-Sheet 3 /(A sin (H 6 k/l cos PHASE INTEGRA TOR /N TEGPATOR lN VER TER 5 EX 5 G U p H 6A TE 7 /20 moss/Ne R915 6 Ex INDICATOR GATE!) FLOP oscumrok 26 54 20 ilN/T/AT/NG &

PULSE cvcuz COUNTER 27 kA sin (wH T\'- G) M1 C05 (wf 19) PHASE D/FFERM f/A me DIFFERENT/M03 |NVEQTER By 4 Ex E 6 ZE o x 0205s we 24 INDICATOR FLIP'FLOP s/meo h, 25 E OSCILLATOR INITIATING 4 PULSE yC E N 27 63 COUNTER INVENTOR Herbe/"z D. 600k V xazxw ATTORNEY United States Patent 3,27tl,189 DEVICE FOR DETERMINING AN ANGLE FROM A SET OF GRTHQGUNAL CGMPQNENTS Herbert D. Cools, Arlington, Va, assignor to the United States of America as represented by the Esecretary of Commerce Filed Italy 7, 1961, Ser. No. 122,600 4 Claims. (Cl. 235-189) This invention relates to an electrical device for indicating the angle of a radius vector when signals dependent upon a set of orthogonal components are applied thereto.

The systems in the prior art, used for measuring the angle of a radius vector when signals dependent upon a set of orthogonal components are known, employ electromechanical devices, such as resolvers or servomechanisms and therefore are relatively slow in making computations.

Accordingly, it is an object of the present invention to provide a device, comprising primarily electrical and electronic components, for rapidly converting signals representing the orthogonal components of a point to a signal representing the angle of a radius vector drawn through the point.

This is accomplished by using a pair of signals having substantially constant magnitudes proportional to the y and x components, to generate a waveform, for example,

kA cos(wt+0) where A- /x +y and k is an arbitrary constant. The phase difference between kA COS(wt+l9) and cos wt is then measured to determine the value of (9.

In the figures:

FIG. 1 is a vector diagram used in explaining the operation of the invention;

FIG. 2 is a first embodiment of the invention;

FIGS. 3A to 3D are waveforms used in explaining the operation of the invention;

FIG. 4 is a second embodiment;

FIG, 5 'is a third embodiment; and

FIG. 6 is a fourth embodiment of the present invention.

Referring to FIG. 1, point P is located on radius vector A which is drawn at an angle 0 through the origin. The x component of point P is equal to A cos 0, and the y component is equal to A sin 0. The components are obtained as analogue values from a system, not shown, in which their values are always related by the expression A= /x +y In FIG. 2, a signal dependent upon the value of the angle 6 is obtained in three steps. First, waveform k sin wt is multiplied by a signal having a substantially constant magnitude proportional to A sin 6, and waveform k cos wt is multiplied by a signal having a substantially constant magnitude proportional to A cos 6. (k and w are chosen arbitrarily.) Next, the sum or difierence of these products is obtained, the result being expressed by the trigonometrical equations:

A cos 6 cos wt-i-kA sin 0 sin wt=kA cos (wt-0) A cos 0 cos wtkA sin 0 sin wt=kA cos (wt-H9) Cos (wt-0) and cos (wt+0) are sinusoidal functions of wt, whose phase with respect to cos wt varies directly with 6. The third step, therefore, is to measure the difference in phase between kA cos (wt-0) or kA cos (wt-|-0) and A cos wt. This measurement indicates the value of 6.

Referring to FIG. 2, a substantially constant voltage B having a magnitude proportional to A sin 0 is applied to terminals 10 so that current flows through normally-closed gate 11, resistor 12 and inductor 13 to ground. At the same time, a substantially constant voltage E having a magnitude proportional to A cos 0, applied to terminals 14, causes current flow through resistor 15, inductor 16 and capacitor 17 to ground. Capacitor 17 is then charged to a voltage having a magnitude equal to that on terminals 14. A sin 0 and A cos 0 have magnitudes equal to the values of the orthogonal components of point P in FIG. 1.

At Zero time t a pulse, applied to terminals 19, operates flip-flop 20 to provide a signal that starts gated oscillator 26, opens gate 11 and closes normally-open gate 18. When gate 11 opens, the parallel circuit, comprising inductor '13 and capacitor 28, resonates, using the energy stored in the inductor. The sinusoidal voltage appearing across the capacitor has the waveform kA sin 1? sin wt, as shown in FIG. 3A, where kA sin 0 is the amplitude coefficient of sin wt.

When gate 18 closes, the parallel resonant circuit comprising inductor 16 and capacitor 17 is completed. Using the energy stored in capacitor 17, the circuit resonates, developing a voltage across the capacitor that has the waveform kA cos 0 cos wt, FIG. 3B, where kA cos 0 is the amplitude coefiicient of cos wt.

If the arms of switches 21, 22 are in contact with terminals E, E, respectively, waveforms kA sin 0 sin wt and kA cos 0 cos wt are applied to differencing network 23 so that the output of the network has the waveform kA cos (wt+6), FIG. 3C.

The phase difference between waveforms kA cos (wt-F0) and cos wt is obtained by measuring the elapsed between the initiating pulse t and the first zero crossing of kA cos (wt-l-B) of a chosen slope. Hence, the output of differencing network 23 is applied to zero-crossing indicator 24 which provides a pulse at time t when cos (wt-H9) passes the Zero axis from a negative to a positive polarity, as shown in FIG. 3C. The initiating pulse, as stated above, is applied at time t to flip-flop 20 which generates a signal that initiates the operation of gated oscillator 26, and the pulse at time t is applied to the flip-flop which then generates a signal that terminates the operation of the oscillator. Cycle counter 27, connected to the output of the oscillator, counts the number of cycles generated in the time interval between t and t FIG. 3D, which indicates the value of angle 0. If, for example, the angular frequency of oscillator 26 is Nw and the count obtained is M, the value of the angle is 21rM/N radians or 360M/N degrees.

If the arms of switches 21, 22 are in contact with termi nals F, F, respectively, waveforms kA sin 0 sin wt and kA cos 0 cos wt are applied to summing network 30-. The output of the latter, having a waveform kA cos (wt-0), is applied to zero-crossing indicator 24 which applies a signal to flip-flop 20 at time t Cycle counter 27 indicates the number of cycles occurring in the time interval between t and t thereby measuring the value of angle 9, as described immediately above.

It is apparent that indicator 24, flip-flop 2t), gated oscillator 26 and counter 27 cooperate to measure the phase difference between kA c0s(wl+0) or kA cos(wt-0) and cos wt. Other arangements well known in the art could be used tomake this measurement.

Referring to FIG. 4, a substantially constant voltage E having a magnitude proportional to A cos 0 is applied to terminals 40 so that current fiows through resistor 41, capacitor 42 and inductor 43 to ground, charging capacitor 42 to the voltage at terminals 40. A cos 0 has a value equal to the magnitude of the x component of point P in FIG. 1. Simultaneously, a constant voltage B having a magnitude proportional to A sin 0, applied to terminals 44, causes current to fiow through normally closed gate 45, resistor 46 and inductor 43 to ground. A sin 0 has a value equal to magnitude of the y component of point P. At zero time t an initiating pulse applied .to terminals 48 operates flip-flop: 20 which provides a signal that closes normally-open gate 47, opens gate 45 and starts operation of gated oscillator 26.

When gate 47 is closed, voltage E is applied through resistor 41 and gate 47 to ground. The source, not shown, providing this voltage is not shorted to ground because of resistor 41. When gate 4-7 is closed, a parallel resonant circuit is completed that includes capacitor 42 and induct-or 43. The energy stored in the capacitor and inductor force the resonant circuit to oscillate so that in effect k sin wt and k cos at are multiplied by A sin and A cos 0, respectively. The voltage developed across inductor 43 has the waveform kA sin(wt+1r-|-0) and is applied to zero-crossing indicator 24.

As previously mentioned, at time t flip-flop 20 provides a signal that initiates operation of gated oscillator 26; at time I zero-crossing indicator 24 operates flip-flop 20 to provide :a signal that terminates operation of oscillator 26. Counter 27 indicates the number of cycles occurring in the time interval between t and t which is a measure of the angle 0, as described above in connection with FIG. 2.

Referring to FIG. 5, integrators 51, 52 and phase inverter 53 are connected in a loop. A substantially constant voltage E having a magnitude proportional to A cos 0 is applied to terminal 54, While a substantially constant voltage B having a magnitude proportional to A sin 0 is applied to terminal 55. A cos 0 and A sin 0 have values equal to the magnitudes of the x and y cornponents, respectively, of point P in FIG. 1. When an initiating pulse is applied at zero time t to flip-flop 20, the latter generates a signal which closes normally-open gate 56. A sin 0 is then applied to the input and A cos 0 to the output of integrator 51.

When the arm of switch 57 is in contact with terminal G, waveform kA sin(wt+0) is applied to zero-crossing indicator 24; and when the arm is in contact with terminal H, waveform kA cos(wt+6) is applied to the indicator. As in the embodiments previously described, at time t flip-flop 20 generates a signal to initiate operation. of gated oscillator 26; at time i indicator 24 controls the flip-flop to generate a signal to terminate operation of the oscillator. Counter 27, indicating the number of cycles that occur in the time interval between t and t measures the angle 0, as described in connection with FIG. 2.

Referring to FIG. 6, differentiators 60, 61 and phase inverter 62 are connected in a loop. Substantially constant voltages E and B having magnitudes proportional to A cos 6 and A sin 0, respectively, are applied to terminals 62, 63. A sin 0 and A cos 9 have values equal to those of the orthogonal components of point P in FIG. 1. At time t an initiating pulse controls flip-flop 20 to provide a signal that closes normally-open )gate 64. Voltage E is then fed to the input and voltage E to the output of difierentiator 60. Simultaneously, the signal provided by the flip-flop is applied to gated oscillator 26, initiating operation of the oscillator.

When the arm of switch 65 is in contact with terminal J, wavefrom kA cos-t (wZ0) is applied to indicator 24; when the \arm is in contact with terminal M, wavefrom kA sin(wt+1r0) is applied to the indicator. At time I indicator 24 feeds a pulse to flip-flop 20 to generate a signal that opens gate 64 and terminates operation of oscillator 26. As in the other embodiments, counter 27 indicates the number of cycles occur-ring in the time interval between t and t which is a measure of the angle 0.

Obviously, many modifications and variations are possible in the light of the above teachings. For example, in FIG. the signals applied to switch 57 could be derived from any one of several points in the loop comprising integrators 51, 52 and phase inverter 53, or voltage E could be applied to the output and voltage E to the input of integrator 51. In the latter case, the signals applied to switch 57 would have different waveforms than shown, but the results achieved would be essentially the same. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.

I claim:

1. In a device for measuring the angle of a radius vector, a first input terminal, a first parallel resonant circuit, a normally-closed gate connected between said first terminal and said first resonant circuit, a second parallel resonant circuit comprising an inductor, a capacitor and a normally-open gate connected in a loop, a second input terminal connected to said second resonant circuit, a differencing network connected between said first and second resonant circuit and phase measuring means connected to the output of said differencing network.

2. In a device for measuring the angle of a radius vector, a first input terminal, a first parallel resonant circuit, a normally-closed gate connected between said first ter minal and said first resonant circuit, a second parallel resonant circuit comprising an inductor, a capacitor and a normally-open gate connected in a loop, a second input terminal connected to said second resonant circuit, a summing network connected between said first and second resonant circuit and phase measuring means connected to the output of said summing network.

3. In a device for measuring the angle of a radius vector, a first input terminal, a first parallel resonant circuit, a normally-closed gate connected between said first terminal and said first parallel resonant circuit, a second parallel resonant circuit comprising an inductor, a capacitor and a normally-open gate connected in a loop, a second input terminal connected to said second resonant circuit, a differencing network connected between said first and second resonant circuit, a zero-crossing indicator having an input connected to the output of said diiferencing network, a flip-flop circuit having an input connected to the output of said zero-crossing indicator, a third terminal connected to the input of said fiip-flop circuit, a gated oscillator, means for applying the output of said flip-flop circuit to the said normally-open gate, said normallyclosed gate and said oscillator, and a cycle counted connected to the output of said oscillator.

4. In a device for measuring the angle of a radius vector, a first input terminal, a first parallel resonant circuit, a normally-closed gate connected between said first input terminal and said first parallel resonant circuit, a second parallel resonant circuit comprising an inductor, a capacitor and a normally-open gate connected in a loop, a second input terminal connected to said second resonant circuit, a summing network connected between said first and second resonant circuit, a zero-crossing indicator having an input connected to the output of said summing network, a flip-flop circuit having an input connected to the output of said zero-crossing indicator, a third terminal connected to the input of said flip-flop circuit, a gated oscillator, means for applying the output of said flip-flop circuit to said normally-open gate, said normally-closed gate and said oscillator, and a cycle counter connected to the output of said oscillator.

fftcon References Cited by the Examiner UNITED STATES PATENTS 2,634,909 4/1953 Lehmann 23561.5 2,812,435 11/1957 Lyon 32483 2,926,852 3/1960 Bennett 235-189 2,939,081 5/1960 Dennis 328-122 OTHER REFERENCES IBM Technical Disclosure Bulletin (Moore), vol. 3, No. 2, July 1960, page 35.

MALCOLM A. MORRISON, Primary Examiner.

DARYL W. COOK, Examiner.

K. W. DOBYNS, Assistant Examiner. 

1. IN A DEVICE FOR MEASURING THE ANGLE OF A RADIUS VECTOR, A FIRST INPUT TERMINAL, A FIRST PARALLEL RESONANT CIRCUIT, A NORMALLY-CLOSED GATE CONNECTED BETWEEN SAID FIRST TERMINAL AND SAID FIRST RESONANT CIRCUIT, A SECOND PARALLEL RESONANT CIRCUIT COMPRISING AN INDUCTOR, A CAPACITOR AND A NORMALLY-OPEN GATE CONNECTED IN A LOOP, A SECOND INPUT TERMINAL CONNECTED TO SAID SECOND RESONANT CIRCUIT, A DIFFERENCING NETWORK CONNECTED BETWEEN SAID FIRST AND SECOND RESONANT CIRCUIT AND PHASE MEASURING MEANS CONNECTED TO THE OUTPUT OF SAID DIFFERENCING NETWORK. 